LEADER 04587nam 2200577 450 001 9910827882003321 005 20230120014710.0 010 $a1-4832-5798-3 035 $a(CKB)3710000000200877 035 $a(EBL)1901722 035 $a(SSID)ssj0001267046 035 $a(PQKBManifestationID)12485360 035 $a(PQKBTitleCode)TC0001267046 035 $a(PQKBWorkID)11254735 035 $a(PQKB)11626260 035 $a(MiAaPQ)EBC1901722 035 $a(EXLCZ)993710000000200877 100 $a20150202h19921992 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 00$aMathematical methods in computer aided geometric design II /$fedited by Tom Lyche, Larry L. Schumaker 205 $aUnited Kingdom edition. 210 1$aSan Diego, California ;$aLondon, England :$cAcademic Press, Inc.,$d1992. 210 4$dİ1992 215 $a1 online resource (649 p.) 300 $aDescription based upon print version of record. 311 $a1-322-55963-5 311 $a0-12-460510-9 320 $aIncludes bibliographical references. 327 $aFront Cover; Mathematical Methods in Computer Aided Geometric Design II; Copyright Page; Table of Contents; PREFACE; PARTICIPANTS; Chapter 1. Symmetrizing Multiaffine Polynomials; 1. Introduction and Motivation; 2. Cubics; 3. Quartics, Quintics, and Sextics; 4. Observations on Conversion to B-spline Form; 5. Open Questions; References; Chapter 2. Norm Estimates for Inverses of Distance Matrices; 1. Introduction; 2. The Univariate Case for the Euclidean Norm; 3. The Multivariate Case for the Euclidean Norm; 4. Fourier Transforms and Bessel Transforms 327 $a5. The Least Upper Bound for Subsets of the Integer GridReferences; Chapter 3. Numerical Treatment ofSurface-Surface Intersection and Contouring; 1. Introduction; 2. Lattice Evaluation(2D Grid-Methods); 3. Marching Based on Davidenko's Differential Equation; 4. Marching Based on Taylor Expansion; 5. Conclusion and Future Extensions; References; Chapter 4. Modeling Closed Surfaces:A Comparison of Existing Methods; 1. Introduction; 2. Subdivision Schemes; 3. Discrete Interpolation; 4. Algebraic Interpolation; 5. TransfiniteInterpolation; 6. Octree and Face Octree Representations 327 $a7. Discussion of These Modeling SchemesReferences; Chapter 5. A New Characterization of PlaneElastica; 1. Introduction; 2. A Characterization of Ela?stica by their Curvature Function; 3. A Characterizing Representation Theorem; References; Chapter 6. POLynomials, POLar Forms, and InterPOLation; 1. Introduction; 2. Algebraic Definition of Polar Curves; 3. Interpolation; 4. Conclusion and a Few Historical Remarks; Chapter 7. Pyramid Patches ProvidePotential Polynomial Paradigms; 1. Introduction; 2. Linear Independence of Families of Lineal Polynomials; 3. B-patches for Hn(IRs) 327 $a4. Other Pyramid Schemes5. B-patches for IIn(IRs); 6. Degree Raising, Conversion and Subdivision for B-patches; References; Chapter 8. Implicitizing Rational Surfaces with Base Points by Applying Perturbations and theFactors of Zero Theorem; 1. Introduction; 2. Mathematical Preliminaries; 3. The Factors of Zero Theorem; 4. Implicitization with Base Points Using the Dixon Resultant; 5. An Implicitization Example; 6. Conclusion and Open Problems; References; Chapter 9. Wavelets and Multiscale Interpolation; 1. Introduction; 2. Wavelets and MultiresolutionAnalysis 327 $a3. Fundamental Scaling Functions4. Symmetric and Compactly Supported Scaling Functions; 5. Subdivision Schemes; 6. Regularity; References; Chapter 10. Decomposition of Splines; 1. Introduction; 2. Decomposition; 3. Decomposing Splines; 4. Box Spline Decomposition; 5. Data Reduction by Decomposition; References; Chapter 11. A Curve Intersection Algorithm with Processing of Singular Cases: Introductionof a CHpping Technique; 1. Introduction; 2. Clipping; 3. Singular Cases; 4. Examples; 5. Extension to Surfaces; 6. Conclusion; References 327 $aChapter 12. Best Approximations of ParametricCurves by Splines 330 $aMathematical Methods in Computer Aided Geometric Design II 606 $aGeometry$xData processing$vCongresses 615 0$aGeometry$xData processing 676 $a516/.15/0285 702 $aLyche$b Tom 702 $aSchumaker$b Larry L. 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910827882003321 996 $aMathematical Methods in Computer Aided Geometric Design II$9375979 997 $aUNINA